﻿ 状态时滞的离散线性系统的能控性分析 Controllability of Linear Discrete-Time Systems with Time-Delay in State

Vol.04 No.02(2015), Article ID:15173,6 pages
10.12677/AAM.2015.42011

Controllability of Linear Discrete-Time Systems with Time-Delay in State

Juanjuan Zhang, Caixia Gao

School of Mathematical Sciences, Inner Mongolia University, Hohhot Inner Mongolia

Received: Apr. 15th, 2015; accepted: Apr. 29th, 2015; published: May 5th, 2015

ABSTRACT

In this paper, a data-based method is used to analyze the controllability of linear discrete-time systems with time-delay in state. By this method, one can directly construct a controllability matrix using the measured state data without identifying system parameters. Hence, one can save time in practice and avoid corresponding identification errors. Moreover, it is feasible to the study of characteristics of deterministic systems.

Keywords:Controllability, Time-Delay in State, Linear Discrete-Time System, Data-Based Method

1. 引言

2. 预备知识与主要引理

(1)

(2)

(3)

，则是系统(1)的能控矩阵。

3. 状态时滞的离散线性系统的能控性分析

(4)

(5)

，且。对于第组测试，相应的输入为

(6)

(7)

(8)

(9)

，由引理3和引理4可知，系统(1)是能控的，证毕。

(10)

，则方程(10)可写成

(11)

(12)

(13)

4. 算例

(14)

1) 传统方法

(15)

2) 基于数据方法

，而且如果把上面矩阵的元素四舍五入到小数点后一位，则上面矩阵变为

(16)

5. 总结

Controllability of Linear Discrete-Time Systems with Time-Delay in State. 应用数学进展,02,83-89. doi: 10.12677/AAM.2015.42011

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